Exact results for curvature-driven coarsening in two dimensions

We consider the statistics of the areas enclosed by domain boundaries (`hulls') during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than $A$ has, for large time $t$, the scaling form $N_h(A,t) = 2c/(A+\lambda t)$, demonstrating the validity of dynamical scaling in this system, where $c=1/8\pi\sqrt{3}$ is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of $A/\lambda t$. Identical forms are obtained for coarsening from a critical initial state, but with $c$ replaced by $c/2$.Comment: 4 pages, 4 figure

Geometric properties of two-dimensional coarsening with weak disorder

The domain morphology of weakly disordered ferromagnets, quenched from the high-temperature phase to the low-temperature phase, is studied using numerical simulations. We find that the geometrical properties of the coarsening domain structure, e.g., the distributions of hull enclosed areas and domain perimeter lengths, are described by a scaling phenomenology in which the growing domain scale R(t) is the only relevant parameter. Furthermore, the scaling functions have forms identical to those of the corresponding pure system, extending the 'super-universality' property previously noted for the pair correlation function.Comment: 6 pages, 6 figure

Curvature-driven coarsening in the two dimensional Potts model

We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the $q$-states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with non-conserved order parameter. We analyze the distribution of hull enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for $q=2$ (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit super-universality properties.Comment: 12 pages, 16 figure

Time-resolved photometry of the young dipper RX~J1604.3-2130A:Unveiling the structure and mass transport through the innermost disk

Context. RX J1604.3-2130A is a young, dipper-type, variable star in the Upper Scorpius association, suspected to have an inclined inner disk, with respect to its face-on outer disk. Aims. We aim to study the eclipses to constrain the inner disk properties. Methods. We used time-resolved photometry from the Rapid Eye Mount telescope and Kepler 2 data to study the multi-wavelength variability, and archival optical and infrared data to track accretion, rotation, and changes in disk structure. Results. The observations reveal details of the structure and matter transport through the inner disk. The eclipses show 5 d quasi-periodicity, with the phase drifting in time and some periods showing increased/decreased eclipse depth and frequency. Dips are consistent with extinction by slightly processed dust grains in an inclined, irregularly-shaped inner disk locked to the star through two relatively stable accretion structures. The grains are located near the dust sublimation radius (similar to 0.06 au) at the corotation radius, and can explain the shadows observed in the outer disk. The total mass (gas and dust) required to produce the eclipses and shadows is a few % of a Ceres mass. Such an amount of mass is accreted/replenished by accretion in days to weeks, which explains the variability from period to period. Spitzer and WISE infrared variability reveal variations in the dust content in the innermost disk on a timescale of a few years, which is consistent with small imbalances (compared to the stellar accretion rate) in the matter transport from the outer to the inner disk. A decrease in the accretion rate is observed at the times of less eclipsing variability and low mid-IR fluxes, confirming this picture. The v sin i = 16 km s(-1) confirms that the star cannot be aligned with the outer disk, but is likely close to equator-on and to be aligned with the inner disk. This anomalous orientation is a challenge for standard theories of protoplanetary disk formation.Science & Technology Facilities Council (STFC): ST/S000399/1. ESO fellowship. European Union (EU): 823 823. German Research Foundation (DFG): FOR 2634/1 TE 1024/1-1. French National Research Agency (ANR): ANR-16-CE31-0013. Alexander von Humboldt Foundation. European Research Council (ERC): 678 194. European Research Council (ERC): 742 095. National Aeronautics & Space Administration (NASA). National Science Foundation (NSF). National Aeronautics & Space Administration (NASA): NNG05GF22G. National Science Foundation (NSF): AST-0909182, AST-1 313 422

Kibble-Zurek mechanism and infinitely slow annealing through critical points

We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second order phase transition. We elucidate the time and cooling rate dependence of the typical growing length and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.Comment: 5 pages, 4 fig

Topics in coarsening phenomena

These lecture notes give a very short introduction to coarsening phenomena and summarize some recent results in the field. They focus on three aspects: the super-universality hypothesis, the geometry of growing structures, and coarsening in the spiral kinetically constrained model.Comment: Lecture notes. Fundamental Problems in Statistical Physics XII, Leuven, Aug 30 - Sept 12, 200

Designing international public sector accounting standards: An analysis of constituents’ participation through comment letters

Harmonization of public sector accounting is attracting increasing attention from scholars and practitioners. A focal component of this phenomenon is the setting of accounting standards, whose legitimacy is paramount to their application. As participation by constituents is considered fundamental for ensuring this legitimacy, in this study, we focus on participation through comment letters in the due process. In particular, we explore the type of respondents, their geographical area, their agreement/disagreement with the documents prepared by the International Public Sector Accounting Standards Board (IPSASB) and the issues of importance to them, through an analysis of the comment letters submitted for six projects launched over the period 2017–2020 by the IPSASB. Furthermore, we analyze some factors that may affect countries’ participation in the due process. The analysis enriches our understanding of the IPSASB’s due process and provides relevant insights for the growing research into accounting standard-setting

New algorithms for optimizing and linking conical intersection points

In this paper we present two new algorithms to study the extended nature of the crossing seam between electronic potential energy surfaces. The first algorithm is designed to optimize conical intersection geometries: both minima and saddle points. In addition, this method will optimize conical intersection geometries using arbitrary geometrical constraints. We demonstrate its potential on different crossing seams of benzene, z-penta-3,5-dleniminium, and 1,3-butadiene. The second algorithm is designed to explicitly compute the intersection-space minimum energy coordinate. Our computations show how an intersection seam and the energy along it can be unambiguously defined. A finite region of the S0/S11,3-butadiene crossing seam has been mapped out, and a new saddle point linked with two lower-lying geometries on the sea

Slow Cooling of an Ising Ferromagnet

A ferromagnetic Ising chain which is endowed with a single-spin-flip Glauber dynamics is investigated. For an arbitrary annealing protocol, we derive an exact integral equation for the domain wall density. This integral equation admits an asymptotic solution in the limit of extremely slow cooling. For instance, we extract an asymptotic of the density of domain walls at the end of the cooling procedure when the temperature vanishes. Slow annealing is usually studied using a Kibble-Zurek argument; in our setting, this argument leads to approximate predictions which are in good agreement with exact asymptotics.Comment: 6 page

Geometry of phase separation

We study the domain geometry during spinodal decomposition of a 50:50 binary mixture in two dimensions. Extending arguments developed to treat non-conserved coarsening, we obtain approximate analytic results for the distribution of domain areas and perimeters during the dynamics. The main approximation is to regard the interfaces separating domains as moving independently. While this is true in the non-conserved case, it is not in the conserved one. Our results can therefore be considered as a first-order approximation for the distributions. In contrast to the celebrated Lifshitz-Slyozov-Wagner distribution of structures of the minority phase in the limit of very small concentration, the distribution of domain areas in the 50:50 case does not have a cut-off. Large structures (areas or perimeters) retain the morphology of a percolative or critical initial condition, for quenches from high temperatures or the critical point respectively. The corresponding distributions are described by a $c A^{-\tau}$ tail, where $c$ and $\tau$ are exactly known. With increasing time, small structures tend to have a spherical shape with a smooth surface before evaporating by diffusion. In this regime the number density of domains with area $A$ scales as $A^{1/2}$, as in the Lifshitz-Slyozov-Wagner theory. The threshold between the small and large regimes is determined by the characteristic area, ${\rm A} \sim [\lambda(T) t]^{2/3}$. Finally, we study the relation between perimeters and areas and the distribution of boundary lengths, finding results that are consistent with the ones summarized above. We test our predictions with Monte Carlo simulations of the 2d Ising Model.Comment: 10 pages, 8 figure